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The Sun’s Polar Magnetic Flux 1996-2006 Observed with SOHO/MDI

The Sun’s Polar Magnetic Flux 1996-2006 Observed with SOHO/MDI. J. Todd Hoeksema E.E. Benevolenskaya, Y. Liu P.H. Scherrer & X.P. Zhao Stanford University. Figure 1

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The Sun’s Polar Magnetic Flux 1996-2006 Observed with SOHO/MDI

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  1. The Sun’s Polar Magnetic Flux 1996-2006 Observed with SOHO/MDI J. Todd Hoeksema E.E. Benevolenskaya, Y. Liu P.H. Scherrer & X.P. Zhao Stanford University Solar Polar Flux – 1996-2006 - MDI

  2. Figure 1 • Apparent values of the magnetic flux of the radial field component in the latitude zones from 78o to 88o in Northern (blueline) and Southern (redline) hemispheres • The fraction of positive polarity magnetic flux in Northern(blueline) and Southern (redline) hemispheres • c) Total signed magnetic flux. The polar magnetic field reversal was in CR1975± 2 (April 2001) in the North and in CR1981± 2 (September 2001) in South. Figure 1 Solar Polar Flux – 1996-2006 - MDI

  3. The apparent values of the total unsigned magnetic flux Fr = |F+| + |F-| for the polar caps 78o – 88o are presented in Figure 1a for reduced-resolution synoptic maps (1o in both latitude and longitude). There is a N-S asymmetry in the distributions of the total polar magnetic flux for low-resolution maps: Fr = 1.5-1.8 x 1022 Mx and Fr = 2.0-2.5 x 1022 Mx for the North and South polar caps before CR2007 (September 2003). After that, the total magnetic flux increases slightly in North and decreases in the South. The positive |F+| /Fr fraction of the magnetic flux is plotted in Figure 1b. Total signed flux is present in Figure 1c. The time of reversals can be easily determined at |F+| /Fr = 0.5. This was in CR1974 (March 2001) in theNorthand in CR1980 (August 2001) inSouth. This is close to the periods obtained by Durrant and Wilson ( Solar Physics, 2003): CR1975 inNorthand CR1981 inSouthusing the Kitt Peak synoptic maps. Figure 1 Solar Polar Flux – 1996-2006 - MDI

  4. SOHO Rotated a) c) Magnetic Field Observational Variation d) b) SOHO Nominal Figure 2 Solar Polar Flux – 1996-2006 - MDI

  5. Figure 2 -MDI Spatial Noise Pattern Left column: Magnetic maps averaged over 60 min periods a) Upper: B whenSOHO/MDIwasrotated, P_angle = 180.0o. b) Lower: B whenSOHO/MDIwasnot rotated, P_angle = 0.0o. Right Column: The Noise level as σ- distribution of 1 min images in 60 min series: c) Upper: σ-distributionwhenSOHO/MDIwasrotated, P_angle = 180.0o d) Lower: σ-distributionwhenSOHO/MDIwasnot rotated, P_angle = 0.0o Figure 3 – MDI Noise for 5-min and 1-min Magnetograms One-hour noise level along the central meridian as σ-distribution for the two kinds of MDI magnetograms Left: images averaged over 5 minutes on-board (a, c) and Right: 1 min magnetograms (b, d) for two time sets in 1 hour series. Upper: SOHO/MDI was rotated. Lower: SOHO/MDI was not rotated. Figure 2, 3 Solar Polar Flux – 1996-2006 - MDI

  6. N-S sigma distributions along CM 5min Mags 1min Mags MDI Rotated MDI Nominal Figure 3 Solar Polar Flux – 1996-2006 - MDI

  7. Figure 4. Variations of the value of apparent total unsigned flux as function of the number of images averaged for the polar caps: a) forNorth and b) for South Figure 5. Synoptic magnetic maps of CR2027 (25 February – 25 March, 2005) a) is constructed from a single image at each point, i.e. without any averaging. b) is constructed by averaging 60 images at each point. Latitude in sin (latitude). Resolution is 1o in both latitude and longitude. Figure 6. Noise level (σ – distribution) versus latitude for CR 1993 and CR 2020 for 5 min and 1 hour averaged magnetograms. a)σ=9.3G for 87oN-88oN and σ=10.7G for 80oS-81oS; (P_angle = 0.0o) b)σ=2.7G for 87oN-88oN andσ=4.8G for 80oS-81oS; (P_angle = 0.0o) c) σ=9.7Gfor 87oN-88oN andσ=12.3G for 80oS-81oS; (P_angle = -180.0o) d)σ=3.9G for 87oN-88oN and σ=4.8G for 80oS-81oS; (P_angle = -180.0o) Solar Polar Flux – 1996-2006 - MDI

  8. The apparent total unsigned magnetic flux of polar caps, 78-88o computed using various numbers of averaged images during favorable polar viewing conditions. NORTH: CR1993-Aug 2002; CR2020-Aug 2004; CR2033-Aug 2005 SOUTH: CR1960-Mar 2000;CR2013-Feb 2004; CR 2027-Mar 2005 P-angle = 180 for CR 2013, CR2020, CR2027 & CR 2033 P-angle = 0 for CR 1960 and CR 1993 Figure 4 Solar Polar Flux – 1996-2006 - MDI

  9. Single Mag Sine 60 Mags Sine Figure 5 Solar Polar Flux – 1996-2006 - MDI

  10. SOHO Nominal SOHO Rotated Figure 6 Solar Polar Flux – 1996-2006 - MDI

  11. The value of the apparent total polar magnetic flux depends on the number of averaged images (Figures 4, 5). The pixel noise level of the MDI magnetograms was estimated by Ortiz et.al (2002). The 1-σ noise level for 1-min longitudinal magnetograms is 20 G. The magnetic noise level for 5-min magnetograms is about 9G. The random noise level decreases as 1/√N, where N is number of observations. The noise level is 2.8G for 50 min and 2.6 G for 60 min. They concluded that 20-min averages have a reasonably low noise level. They also noted the increase of the noise in the bottom right of the image, which we can see in Figure 2(c,d). This is caused by systematic errors in the tuning of MDI. There is some discrepancy in the apparent values of the total magnetic flux estimated from synoptic maps obtained from 15 averaged images per day and the consecutive 1 min images averaged for 60 min (see Figures 1a and 4a ). For example, for CR 2033 (8 Aug – 4 Sep 2005) the total magnetic flux was 2.256•1022 Mx for 15 images taken during day but it is higher for any number of averaged images up to N=60. We expect this is connected with the reduction of the supergranulation noise, which is more completely suppressed in the first case. Solar Polar Flux – 1996-2006 - MDI

  12. The effect of MDI shutter noise on the apparent polar magnetic flux. The shutter noise of the SOHO/MDI instrument induces a small random offset into the magnetic measurements that is uniform over the disk. (Liu, Zhao & Hoeksema, 2004). The offset is removed from each magnetogram. We have estimated the magnetic flux of north polar cap (78oN-88oN) during the CR2033withoffset correction and withoutoffset correction. There is a small difference in the relative positive magnetic flux and magnetic strength. Withcorrectionwe obtain(|F+|/ Fr)= 0.3616 and the averaged radial component of the magnetic field is Br =- 8.13G. Without the correction(|F+|/ Fr)= 0.3676and the averaged radial component of the magnetic field is Br = -7.62G. There is only a small difference in the apparent total magnetic flux. For example, the total unsigned magnetic flux in CR2021 is 1.7524x 1022 Mx without correction and it is 1.7912x 1022 Mx with correction. Solar Polar Flux – 1996-2006 - MDI

  13. Summary The value of the apparent total magnetic flux depends on the number of averaged magnetograms in the synoptic map. The apparent values decreases with the number of the averaged magnetograms due to random noise reduction. Shutter noise contributes a small portion to the estimation of the total unsigned magnetic flux of polar caps. Systematic errors are not reduced. Individual magnetograms reveal the non-uniformσ-distribution over solar disk. The noise increases to the SW on normal magnetograms, and in the NE when SOHO/MDI is rotated by 180o. Other effects make it difficult to estimate the “true” polar flux. References Benevolenskaya, E.E., 2004, A&A, 428, L5. Durrant, C.J., & P.R. Wilson, 2003, Solar Phys., 214, 23. Liu, Y., X.P. Zhao, & J.T. Hoeksema, 2004, Solar Phys., 219, 39. Ortiz, S.K. Solanki, V. Domingo, M. Fligge, & B. Sanahuja, 2002, A&A, 388, 1036. Solar Polar Flux – 1996-2006 - MDI

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